Molecular Reorientation in Liquids. II. Angular Autocorrelation Functions

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Abstract
The normalized angular autocorrelation functions which appear in the theories of rotational nuclear magnetic and dielectric relaxation are considered in the light of the results presented in Paper I of this series. The time-dependent spherical harmonics in the equations for the autocorrelation functions are written as functions of the molecular Eulerian angular displacements. The time dependence of the autocorrelation functions is calculated using the distribution functions obtained in I, and it is shown that the results are strongly dependent upon the magnitude of the components of the diagonalized rotational friction tensor. If all components are large and unequal, five relaxation times appear in the autocorrelation function for nuclear relaxation and three times appear in the function for dielectric relaxation. If one or more of the components are small, the autocorrelation functions are found to be dependent upon the inertial terms in the molecular equations of motion. Autocorrelation functions are evaluated in the case that all the components of the rotational friction tensor of a spherical top are zero, and an approximate equation for the autocorrelation function is suggested for systems in which dynamical coherence is the predominant factor in the reorientational motion. These equations are Gaussian functions of time, with time constants which depend only upon the inertial properties of the molecule. In principle, the results of this paper, together with the results of I, allow one to compute rotational relaxation behavior in liquids from molecular interaction potential functions.